• Multiplying & Dividing. Basic addition. Helps us get faster.
• You learn your Prime Numbers.
• Overall Number knowledge: Prime Numbers; Factors; Multiples; Square Numbers; Powers.
• There is strategy you can do, sometimes you get lucky.
• Getting to 101 in two turns is FUN!
  • Roll 5&5 followed by 4&1. First turn 5*5= 25 (the other game piece goes to 10); Second turn 25*4=100; 100+1=101
  • Roll 5&5 followed by 1 & any number. First turn 5*5=25 then 25-5=20 then 20*5=100. Second turn 100+1=101 (the other game piece goes on the board)
  • Roll 5&4 followed by 5&1: First turn 5*4=20; Second turn 20*5+1=101
  • Roll 3&11 followed by 3&2: First turn 3*11=33; Second turn 33*3+2=101
  • Investigation: How many ways can you get to 101 in two turns?

Some students felt that keeping under 50 was good because the numbers could be doubled. They felt if you were between 60 and 80 you got stuck adding too often. (Calvin & Ty 9x).

They are going to consider the options for each number between 50 and 85 to see if they can prove their conjecture of a slow zone existing. How many moves is a number from 101? Can we rank numbers using probability and the least number of moves to get to 101?

If there is a SLOW zone, then perhaps there are LUCKY numbers. For example if you are on 33 and get a 3 you can move to 99. (Calvin & Ty).

They are going to look for LUCKY numbers, perhaps even looking at all the numbers on the board and consider how "lucky" they are. Then their strategy will be to get to these numbers rather than just advancing up the board as fast as possible.

• Some students did not want to land on RED Primes, as last time they played all the Prime Cards were bad.
• Other students aimed to land on RED Primes, as they felt the ACTION cards were good and KEEPER Cards were great. They collect KEEPER cards.
• Prove the best strategy using probability. Calculate the number of GOOD cards divided by the total number of cards. This will give us the probability of getting a good Prime Card. Then we can prove which students are correct. Some cards could be good or bad, other are always bad. Work out all the probabilities then decide if landing on a RED prime is a good strategy or not.

• Some students felt that rather than focusing on getting to RED Primes, or to higher numbers, it was better to bump others back to the start.
• One group kept bumping the winning player back to the start and we wondered if this just made the game longer, so it worked in a way.
• How could you prove that bumping people back to the start is the best strategy?
• How can we rank strategies?
• Are multiple strategies better than one?

• Two students spent time thinking of multiple moves then decided which one was best.
• Does this make the game almost as complicated as chess? More complicated due to the element of luck and complex probability?
• Is the only way to prove the best strategies a real life competition? Then talk to the best players?

• Learning to think flexibly when applying operations to numbers.
• Thinking about probabilities.
• Learning to clearly state a conjecture and then attempting to prove the conjecture.